Hydraulic characterization of high temperature hydrocarbon liquid jets

An experimental study has been conducted to investigate the hydraulic characteristics of a plain orifice nozzle issuing pressurized high-temperature liquid hydrocarbon, in order to simulate injection of aviation fuel after being used as coolant in an active cooling system in a hypersonic flight vehicle. The fuel was heated to 553 K (280°C) using an induction heater, at an upstream pressure of up to 1.0 MPa, and injected to atmospheric pressure conditions through a sharp-edged orifice of diameter 0.7 mm and length 4.3 mm. It has been observed that the isothermal lines on the plane of the mass flow rate versus the square root of the pressure drop (ΔP) were clearly affected by increased fuel temperatures, and the discharge coefficient (C_d) decreased sharply with increasing fuel injection temperature (T_inj) above the fuel boiling point of 460 K. The Reynolds number (Re) for three ΔPs with respect to T_inj reached maxima and then began to decrease as T_inj increased for each ΔP case, and the fuel temperature of maximum Re at a given pressure condition increased as ΔP increased. The effects of cavitation on the hydraulic characteristics of the high temperature fuel were explored by representing C_d with respect to three cavitation numbers and dissipation efficiency. The behaviors of C_d showed a clear dependency on cavitation number, and all of the results collapsed to a single curve, regardless of ΔP. In addition, the curve indicated that the C_d characteristics was divided into non-cavitating and cavitating regions by the critical cavitation numbers near the fuel boiling point, and a sharp decrease in C_d was found to be typical in the cavitating region. The relationship between C_d and Re showed that when T_inj exceeded the boiling point the high temperature liquid jets experienced a sharp decrease in C_d at a determined Reynolds number, due to the collapse of the mass flow rate induced by the choked cavitaiton.     

Numerical simulation of wall roughness effects in cavitating flow

Hydrodynamic cavitation has an important effect on the performance of Diesel injectors. It influences the nature of the fuel spray and the efficiency of the combustion process. In the present study, we investigate numerically the effect of wall roughness in the cavitating and turbulent flow developing inside a Diesel injector. The mixture model based on a single fluid is adopted and the commercial Fluent software is used to solve the transport equations.The discharge coefficient C_d is computed for different cavitation numbers and wall roughness heights. Profiles of density mixture, vapor volume fraction, mean velocity and turbulent kinetic energy are reported. The effects of wall roughness and injection pressure are analyzed.     

Transient heating effects in high pressure Diesel injector nozzles

The tendency of today’s fuel injection systems to reach injection pressures up to 3000 bar in order to meet forthcoming emission regulations may significantly increase liquid temperatures due to friction heating; this paper identifies numerically the importance of fuel pressurization, phase-change due to cavitation, wall heat transfer and needle valve motion on the fluid heating induced in high pressure Diesel fuel injectors. These parameters affect the nozzle discharge coefficient (C_d), fuel exit temperature, cavitation volume fraction and temperature distribution within the nozzle. Variable fuel properties, being a function of the local pressure and temperature are found necessary in order to simulate accurately the effects of depressurization and heating induced by friction forces. Comparison of CFD predictions against a 0-D thermodynamic model, indicates that although the mean exit temperature increase relative to the initial fuel temperature is proportional to (1 − C_d²) at fixed needle positions, it can significantly deviate from this value when the motion of the needle valve, controlling the opening and closing of the injection process, is taken into consideration. Increasing the inlet pressure from 2000 bar, which is the pressure utilized in today’s fuel systems to 3000 bar, results to significantly increased fluid temperatures above the boiling point of the Diesel fuel components and therefore regions of potential heterogeneous fuel boiling are identified.     

Vaporization of a liquid hexanes jet in cross flow

The vaporization characteristics of a liquid hexanes jet in a lab-scale test section with a plain orifice-type injector were experimentally investigated. The experimental measurements were carried out on the basis of the infrared laser extinction method using two He–Ne lasers (one at 632.8 nm and the other at 3.39 μm). The momentum flux ratio (q_F/A) was varied from 20 to 60 over 20 steps, and the supplying air temperature (T_A) was changed from 20 to 260 °C over 120 steps. The objectives of the current study were to assess the vaporization characteristics of a liquid hexanes jet and to derive a correlation between flow conditions and hexanes vapor concentration in a jet-in-crossflow configuration. From the results of the experimental measurement, it was concluded that hexanes vapor concentration increased with the increase of the momentum flux ratio and the supplying air temperature. An experimental correlation between flow conditions and hexanes vapor concentration (Z_F) was proposed as a function of the normalized horizontal distance (x/d_o), the supplying air temperature (T_A), the momentum flux ratio (q_F/A), the fuel jet Reynolds number (Re_F), and the fuel jet Weber number (We_F).     

Experimental investigation into the effect of heat transfer on compressible air stream in a duct

A converging nozzle-constant area parallel passage with an outer duct encasing the constant-area passage has been built for investigating the effect of heat transfer on subsonic flow of an air stream. It is concluded experimentally as can be predicted analytically that large quantities of heat are needed in order to accelerate very slow air stream (incompressible) to sonic conditions. It is observed experimentally as confirmed analytically, that the increase in Mach number with heat addition is associated with a decrease in the local static pressure along the axis of the duct. It could be concluded that any more heat added beyond thermal choking will be accompanied by a decrease in the mass flow rate of the compressible flowing air.Nomenclature A cross-sectional area of the duct - C _{P air} specific heat of air joules/kg. °K - C _d discharge coefficient - D duct diameter - d orifice diameter m - dA _d elemental lateral area of the duct - h overall heat transfer coefficient - h head across orifice, mm. - M Mach number - m _air mass flow rate of air - P local static pressure - P _b back pressure at duct outlet - P ₀₁ stagnation pressure at duct inlet - gas density - _u air density upstream of orifice - _q incremental heat flow - T local static temperature - T ₀₁ stagnation temperature at duct inlet - T _h hot water temperature - q heat added per kg of flowing air - V flow speed     

Evaluating cavitation regimes in an internal orifice at different temperatures using frequency analysis and visualization

Experiments on a water cavitating orifice were conducted to investigate the influence of pressure and temperature on flow regime transition due to cavitation. The thermal effects could be important in cases with cryogenic cavitation or hot fluid injection. The investigations were based on CCD observations and a pressure fluctuations frequency analysis.The high-speed photographic recordings were used to analyze the cavitation evolution and individuate the frequency content of the two-phase flow by processing the pixel-intensity time-series data.The cavitating structures showed different behaviors and characteristics with variations in operating conditions, as the pressure inside the orifice and the flow temperature .The flow regime map for the cavitating flow was obtained using experimental observations to analyze the occurrence of the different two-phase flow regime transitions at various operating conditions.As the pressure at the orifice inlet increased, at the same downstream pressure, cavitation inception occurred. The decrease of the cavitation number brought a significant increase in cavitation zone extension. As the pressure drop inside the orifice increased, the cavitation was characterized by an evident increase in cavitation zone length to the outlet of the orifice. With a further cavitation number decrease, the transition to jet cavitation was evident.The temperature influenced both the cavitation intensity and the cavitation number at which different two-phase flow regime transitions occurred, which tended to increase with temperature.The vapor fraction was estimated using an image processing algorithm.The frequency content given by the pressure fluctuations was analyzed and compared with the frequency spectra obtained from the visual observations. The behavior of the different cavitating flows could be correlated to the frequency spectrum of the pressure fluctuations measured upstream and downstream of the orifice. The cavitation number reduction and consequent increase in cavitating area width were related to a corresponding significant increase in the amplitude of typical frequency components. The transition to jet cavitation was characterized by a significant increase in the first peak in the frequency spectrum; weaker spectral peaks were also present at high cavitation numbers.     

Influence of cavitation on blade characteristics

An experimental study of flow around a blade with a modified NACA 4418 profile was conducted in a water tunnel that also enables control of the cavitation conditions within it. Pressure, lift force, drag force and pitching moment acting on the blade were measured for different blade angles and cavitation numbers, respectively. Relationships between these parameters were elaborated and some of them are presented here in dimensionless form. The analysis of results confirmed that cavitation changes the pressure distribution significantly. As a consequence, lift force and pitching moment are reduced, and the drag force is increased. When the cavitation cloud covers one side of the blade and the flow becomes more and more vaporous, the drag force also begins to decrease. The cavity length is increased by increasing the blade angle and by decreasing thé cavitation number.List of symbols A (m²) blade area,B ·L - B (m) blade width - C _D (–) drag coefficient,F _D /(p _d ·A) - C _L (–) lift coefficient,F _L /(P _d ·A) - C _M (–) pitching moment coefficient,M/(P _d ·A ·L) - C _p (–) pressure coefficient, (p-p _r )/p _d - F (N) force - L (m) blade length - M (Nm) pitching moment - p (Pa) local pressure on blade surface - p _d (Pa) dynamic pressure, ·V ²/2 - p _r (Pa) reference wall pressure at blade nose position if there would be no blade in the tunnel - p _v (Pa) vapor pressure - p ₁ (Pa) wall pressure 350 mm in front of thé blade axis - Re (–) Reynolds number,V ·L/v - V (m/s) mean velocity of flow in the tunnel - x (m) Cartesian coordinate along thé blade profile cord - x _c (m) cavity length,x-coordinate of cavity end - (°) blade angle - v (m²/s²) kinematic viscosity - (kg/m³) fluid density - (–) cavitation number, (p _r –p _v )/p _d - (°) angle of tangent to thé blade profile contour     

Study of cavitation phenomena based on a technique for visualizing bubbles in a liquid pressurized chamber

In this paper, the influence of nozzle geometry on cavitation and near-nozzle spray behavior under liquid pressurized ambient is studied. For this purpose, eight steel drilled plates, with different diameters and degrees of conicity of their holes, are analyzed. A special near-nozzle field visualization technique, using a test rig pressurized with fuel, is used. Due to the difference in refractive index between liquid and vapor phase, bubbles present at the outlet of the orifice are visualized. The pressure conditions at which bubbles start appearing at the orifice outlet are compared with those at which choked flow appears. The results showed that pressure conditions for inception of cavitation obtained in the visualization tests differs from those seen for choked flow (5–8% in terms of cavitation number). In addition to this, the images taken are analyzed to get the angle of the jet formed by fuel bubbles, showing that it increases significantly for those conditions more prone to cavitate. Furthermore, comparison of bubbles generation when increasing or decreasing backpressure indicates the presence of hysteresis in cavitation inception phenomena.     

Instantaneous visualization of surface flows

An experimental system is described for visualizing the surface flow of a wing, using an oil smoke tracer technique. The method leads to the determination of the instantaneous velocity direction at the output of surface injectors. A preliminary investigation is made on a flat plate to optimize the conditions of oil smoke injection. Then, the visualization is performed on the upperside of a sweptback wing in the vicinity of the reattachment of the vortex flow. This visualization technique can be applied to other types of wall flows — separated or not — around various bodies.List of symbols b wing span - c _n normal (to leading edge) chord - c _r streamwise (or root) chord - d diameter of the injectors - distance from the apex along the leading edge - relative distance from the apex along the leading edge ( = /C _d) - sweep angle - e injector geometric parameter (e = d/l) - angle of attack - K injection parameter - l length of the injectors - v kinematic viscosity - P _t, P_s total and static pressure of the flow - P _inj injection pressure - P _r reduced pressure (P _r = (P_inj – P_t)/(P_t – P_s)) - Re flow Reynolds number (Re = V ·c _n/v) - Re _i injector Reynolds number (Re = V ·d/v) - s curvilinear distance along c _d - s relative curvilinear distance along c _d(s = s/c _d) - V infinite upstream flow velocity     

The compressible discharge of air through small thick plate orifices

Summary The choking of nozzles at pressure ratios below the critical has long been understood. Knife edge orifices however do not appear to choke. This can be explained and the variation of discharge coefficient with pressure ratio may be calculated. The present paper is an experimental investigation into the discharge through thick plate orifices when the pressure ratio is in the vicinity of its critical value. A comparison is made with the results of other workers and an attempt is made to explain the discharge characteristics of thick plate orifices.Notation C discharge coefficient - D orifice diameter - P absolute static pressure - T thickness of orifice plate Suffixes c critical pressure - d downstream conditions - i incompressible flow conditions - u upstream conditions     

Shadowgraph, Schlieren and interferometry in a 2D cavitating channel flow

Cavitation plays an important role in fuel atomization mechanisms, but the physics of cavitation and its impact on spray formation and injector efficiency are not well documented yet. Experimental investigations are required to support the development and the validation of numerical models and the design of tomorrow??s injectors, in the context of pollutant and fuel consumption reduction. The complexity of modern injectors and the extreme conditions of injection do not facilitate experimental investigations. In this paper, experiments are conducted in a simplified geometry. The model nozzle consists of a transparent 2D micro-channel supplied with a test oil (ISO 4113). Three different optical techniques are proposed to investigate the channel flow, with the pressure drop between upstream and downstream chambers as a parameter. A shadowgraph-like imaging technique allows the observation of cavitation inception and vapor cavities development throughout the channel. The technique also reveals the presence of density gradients (pressure or temperature) in the channel flow. However, this additional information is balanced by difficulties in image interpretation, which are discussed in the paper. In addition, a combination of Schlieren technique and interferometric imaging is used to measure the density fields inside the channel. The three techniques results are carefully analyzed and confronted. These results reveal a wealth of information on the flow, with pressure waves generated by bubble collapses, turbulence in the wake of vapor cavities and bubble survival in flow regions of high pressure. Our results also show that cavitation inception is located in the shear layers between the recirculation zones and the main flow, relatively far from the inlet corner, where the pressure is minimum in average. To explain this behavior, we propose a scenario of cavitation inception based on the occurrence and the growing of instabilities in the shear layers.     

Effect of a Uniform Horizontal Throughflow on the Darcy Free Convection over a Permeable Vertical Plate with Volumetric Heat Generation

This article deals with the steady Darcy free convection adjacent to a heated or cooled permeable vertical flat plate of constant temperature, which is embedded in a fluid-saturated porous medium of uniform ambient temperature T _∞. There is a uniform horizontal throughflow of the fluid and a volumetric heat generation q′′′ takes place, which is considered to be a power-law function of the local temperature difference T ? T _∞, i.e., q′′′ ~ (T ? T _∞) ⁿ . To be specific, two cases of this type of volumetric heat generation are considered in the analysis in some detail, namely, the linear and the quadratic cases, n = 1 and n = 2, respectively.     

Flow characteristics in flow networks

A flow network is a system of mutually intersecting holes in a plate or an assembly of plates. The flow at each intersection is characterized by a collision of two flow streams, resulting in complex flow patterns through the downstream holes. In the case of multiple intersections, the flow is periodically disrupted at each succeeding intersection, thus preventing the formation of a fully-developed flow through the holes.An experimental study is presented in this paper to determine flow characteristics in flow networks with various geometry. The intersecting pressure loss coefficient which represents the performance of flow networks is defined and its magnitude empirically determined as functions of geometric and flow conditions. A method is developed to measure the ramming loss in an intersection tube. Flow visualization by means of hydrogen bubble method is applied to observe flow patterns and mixing behavior in the flow network. A physical model is developed to predict the intersection pressure loss in flow networks.List of symbols A total section area of the flow network holes - a section are a of one hole in the flow network - a _t throat area of the orifice - b semi-minor axis of the intersection throat ellipse (Fig. 8) - C _d overall flow discharge coefficient with intersection - C _do overall flow discharge coefficient in the absence of intersection - D _h hydraulic diameter of the flow channel - d hole diameter - f flow friction coefficient - FF compressible flow function - H major axis of the intersection ellipse (Fig. 8) - K _b, K₀ pressure loss coefficients for the miter bend, and quadrant-edged orifice, respectively - K _c, K_e, K_x flow contraction, expansion, and intersection coefficients, respectively - L length of the hole in the flow network, i.e. flow length inside holes - L _e equivalent length of a pipe for the miter bend pressure loss - N _h number of holes in the flow network - N _x number of intersections for each hole - p pitch distance between holes - P _a, P_s, P_t total pressure in the plenum, the ambient pressure, and absolute total pressure in the plenum, respectively - _Pb, p₀ pressure losses in the miter bend and through the quadrant-edged orifice, respectively - p _T, p_H pressure drops in the flow network and its half unit, respectively - Q, Q flow rates passing through the test section equivalent to standard condition and in operating conditions, respectively - R univeral gas constant - s test plate thickness - T, T _t air temperature in the plenum and the absolute temperature of air, respectively - V fluid flow velocity - W mass flow rate of air - diameter ratio in the quadrant-edged orifice - dynamic viscosity of fluid - kinematic viscosity of fluid - intersection angle between holes - fluid density     

Heat,Water, and Solution Transfer in Unsaturated Porous Media: I -- Theory Development and Transport Coefficient Evaluation

A detailed theory describing the simultaneous transfer of heat, water, and solute in unsaturated porous mediais developed. The theory includes three fully-coupledpartial differential equations. Heat, water, andsolute move in the presence of temperature, T; matricpressure head, _m ; solution osmotic pressure head _o ; and solute concentration C gradients. Thetheory can be applied to describe the mass and energyin radioactive waste repositories, food processing,underground energy storage sites, buried electriccables positions, waste disposal sites, and inagricultural soil. Several transport coefficients forheat, water, and solute are included in the theory. The coefficients are evaluated for a silty clay loamsoil to clarify their dependence on water content (),T, and C. The thermal vapor diffusivity D _Tv first increased as increased to0.22 m³/m³ then decreased with furtherincreases in . D _Tv was 3 orders of magnitudegreater than either isothermal vapor D _mv orosmotic vapor D _ov , diffusivities at of0.20~m³/m³, T of 50°C, and C of 0.001mol/kg. All of the liquid and vapor water transport coefficients increased with increasing T. D _Tv decreased with increasing C to a greater extent thanD _mv and D _ov . The effective thermalconductivity decreased slightly with increasing C. Thesolute diffusion coefficient D _d was 6 to 7orders of magnitude greater than the thermal soluteand salt sieving diffusion coefficients at of0.20~m³/m³, T of 50°C, and C of 0.001 mol/kg.     

A RANS simulation toward the effect of turbulence and cavitation on spray propagation and combustion characteristics

A multidimensional computational fluid dynamic code was developed and integrated with probability density function combustion model to give the detailed account of multiphase fluid flow. The vapor phase within injector domain is treated with Reynolds-averaged Navier–Stokes technique. A new parameter is proposed which is an index of plane-cut spray propagation and takes into account two parameters of spray penetration length and cone angle at the same time. It was found that spray propagation factor (SPI) tends to increase at lower r/d ratios, although the spray penetration tends to decrease. The results of SPI obtained by empirical correlation of Hay and Jones were compared with the simulation computation as a function of respective r/d ratio. Based on the results of this study, the spray distribution on plane area has proportional correlation with heat release amount, NO _x emission mass fraction, and soot concentration reduction. Higher cavitation is attributed to the sharp edge of nozzle entrance, yielding better liquid jet disintegration and smaller spray droplet that reduces soot mass fraction of late combustion process. In order to have better insight of cavitation phenomenon, turbulence magnitude in nozzle and combustion chamber was acquired and depicted along with spray velocity.     

An investigation of possible mechanisms of heterogeneous drag reduction in pipe and channel flows

When concentrated polymer solutions are injected into the core-region of a turbulent pipe or channel flow, the injected polymer solution forms a thread which preserves its identity far beyond the injection point. The resulting drag reduction is called heterogeneous drag reduction.This study presents experimental results on the mechanism of this type of drag reduction. The experiments were carried out to find out whether this drag reduction is caused by small amounts of polymer removed from the thread and dissolved in the near-wall region of the flow or by an interaction of the polymer thread with the turbulence. The friction behavior of this type of drag reduction was measured for different concentrations in pipes of different cross-sections, but of identical hydraulic diameter. The parameters of the injection, i.e. injector geometry as well as the ratio of the injection to the bulk velocity, were varied. In one set of experiments the polymer thread was sucked out through an orifice and the friction behavior in the pipe was determined downstream of the orifice. In another experiment, near-wall fluid was led into a bypass in order to measure its drag reducing properties. Furthermore, the influence of a water injection into the near-wall region on the drag reduction was studied.The results provide a strong evidence that heterogeneous drag reduction is in part caused by small amount of dissolved polymer in the near-wall region as well as by an interaction of the polymer thread with the turbulence.Nomenclature a channel height - b channel width - c _p concentration of the injected polymer solution - c _R effective polymer concentration averaged over the cross-section - d pipe or hydraulic diameter - d _i injector diameter - DR drag reduction - f friction factor - l downstream distance from injector - L length of a pipe segment - P polymer type - p differential pressure - Re Reynolds number - U bulk velocity - u ^* ratio of injection to bulk velocity - y ⁺ dimensionless wall distance - v kinematic viscosity - density of the fluid - _w wall shear stress     

Measurement of atmospheric boundary layer based on super-large-scale particle image velocimetry using natural snowfall

This work intended to study the behavior of the instantaneous vapor fraction in the turbopump inducer of a liquid propellant rocket engine. Experimentations held on an experimental pump test facility and cavitation was attained by reducing the inlet pressure in the machine while maintaining constant the inducer rotational speed. Measurements of vapor fraction through the rotating inducer were achieved by means of an X-ray-based system. The system exerted an industrial X-ray generator and 10 collimated scintillation detectors. Detectors were functioning in current mode thus permitting an acquisition at 5 kHz for each detector. A reference X-ray detector situated between the X-ray generator and the machine permitted the treatment of X-ray beam energy fluctuations related to industrial generators. Acquisitions were performed in three axial positions on the inducer. For each measurement position, three cavitation sequences with different flow rate conditions (Q/Q _n = 0.9, 1, 1.1, where Q _n is the nominal flow rate) were accomplished. Each cycle is performed by decreasing gradually the pressure while maintaining an imposed rotational speed of 4,000 rpm. Each test is constituted of 10 pressure points varying from 2.40 to 0.48 bars representing a complete cavitation sequence. X-ray acquisition was performed for each pressure point, and it was carried out for 10 s thus corresponding to 667 tours of the inducer. Vapor fraction was determined instantaneously thus showing the applicability and the precision of the method in such measurements despite of the geometry and rotation speed constraints. Consequently a quantitative and qualitative evaluation of the vapor fraction is presented. Results show that the vapor distribution is well related to cavitation development on the blades of the inducer for steady cavitation condition.     

Flow regime transitions due to cavitation in the flow through an orifice

This paper presents both experimental and theoretical aspects of the flow regime transitions caused by cavitation when water is passing through an orifice. Cavitation inception marks the transition from single-phase to two-phase bubbly flow; choked cavitation marks the transition from two-phase bubbly flow to two-phase annular jet flow.

It has been found that the inception of cavitation does not necessarily require that the minimum static pressure at the vena contracta downstream of the orifice, be equal to the vapour pressure liquid. In fact, it is well above the vapour pressure at the point of inception. The cavitation number [σ = (P₃ − P_v)/(0.5 pV²); here P₃ is the downstream pressure, P_v is the vapour pressure of the liquid, ρ is the density of the liquid and V is the average liquid velocity at the orifice] at inception is independent of the liquid velocity but strongly dependent on the size of the geometry. Choked cavitation occurs when this minimum pressure approaches the vapour pressure. The cavitation number at the choked condition is a function of the ratio of the orifice diameter (d) to the pipe diameter (D) only. When super cavitation occurs, the dimensionless jet length [L/(D - d); where L is the dimensional length of the jet] can be correlated by using the cavitation number. The vaporization rate of the surface of the liquid jet in super cavitation has been evaluated based on the experiments.

Experiments have also been conducted in which air was deliberately introduced at the vena contracta to simulate the flow regime transition at choked cavitation. Correlations have been obtained to calculate the critical air flow rate required to cause the flow regime transition. By drawing an analogy with choked cavitation, where the air flow rate required to cause the transition is zero, the vapour and released gas flow rate can be predicted.     

Impuls- und Wärmeübertragung bei variablen Stoffwerten für die laminare Plattenströmung

The laminar two-dimensional flow along a flat plate of constant temperature at low velocity is investigated where the temperature dependence of the fluid properties is taken into account. The functions describing the temperature dependence of the fluid properties are expanded as Taylor series at the reference state (preferred free-stream state, but wall state also possible), whose coefficients are dimensionless fluid properties like the Prandtl number, but are not specified for particular fluids. Shear stress and heat flux at the wall are given for arbitrary temperature dependence of the fluid properties as universal power series of the parameter ε=(T_w?T_∞)/T_∞. For all fluids it is shown, how the exponents in the propertyratio method and the reference temperature in the referencetemperature method depend on the fluid properties. Hence, these two methods are not empirical ones any more.     

Finite difference analysis of unsteady natural convection flow along an inclined plate with variable surface temperature and mass diffusion

An analysis is performed to study the transient laminar natural convection flows along an inclined semi-infinite flat plate in which the wall temperatureT _w ^′ and species concentration on the wallC _w ^′ vary as the power of the axial co-ordinate in the formT _w ^′ (x)=T _∞ ^′ +ax ⁿ andC _w ^′ =C _∞ ^′ +bx ^m respectively. The dimensionless governing equations considered here are unsteady, two-dimensional, coupled and non-linear integro-differential equations. A finite difference scheme of Crank-Nicolson type is employed to solve the problem. The velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number are studied in detail for various sets of values of parameters. Correlation equations are also established for Nusselt number and Sherwood number in terms of parameters.